Use newton's method to find the second and third approximation of a root of x3+x+2=0 starting with x1=−1 as the initial approximation. the second approximation is x2 = -18/13 the third approximation is x3 =

The third approximation is

Step-by-step explanation:

We are given that  

We have to find the second and third approximation of a root of given equation by using Newton's method.

We know that Newton's method , if nth approximation is given and then, the next approximation is given by  

Substitute

Substitute the value n=1 then, we get  

Substitute the values then , we get  the second approximation

For n=2

Hence, the third approximation is

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9

do it yourself this is easy

step-by-step explanation: